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Logarithm Word Problem

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In January, the Richter scale measured an earthquake of magnitude 3.2. A month later, in February, you hear on the news that there has been another earthquake, which is 27 times more intense than the one in January. What is the magnitude of the second earthquake?

Oct 28, 2017

#1
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Go online to this USGS site which explains the difference between "intensity" and "magnitude" of an earthquake.  https://earthquake.usgs.gov/learn/topics/mag_vs_int.php

Oct 28, 2017
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Use this formula to find the Magnitude of the earthquake:

E=10^[1.5M + 4.8], where E=Equivalent Energy, M=Richter Scale Magnitude.

E=10^[1.5*3.2 + 4.8]

E=10^[4.8 + 4.8]

E=10^[9.6]

E=3,981,071,705.5 Joules - energy-equivalent of 3.2 magnitude earthquake.

3,981,071,705.5 x 27 =10^[(1.5*M) + 4.8], solve for M

1.07489×10^11 = 10^(1.5 M + 4.8)

1.07489×10^11 = 10^(1.5 M + 4.8) is equivalent to 10^(1.5 M + 4.8) = 1.07489×10^11:
10^(1.5 M + 4.8) = 1.07489×10^11

Take the logarithm base 10 of both sides:
1.5 M + 4.8 = 11.0314

Subtract 4.8 from both sides:
1.5 M = 6.23136

Divide both sides by 1.5:
M = 4.15424 - The magnitude of an earthquake 27 times the intensity of 3.2 magnitude.

Oct 28, 2017